We use results from a 6-th order Taylor expansion of the QCD equation of
state to construct expansions for cumulants of conserved charge fluctuations
and their correlations. We show that these cumulants strongly constrain the
range of applicability of hadron resonance gas model calculations. We point out
that the latter is inappropriate to describe equilibrium properties of QCD at
zero and non-zero values of the baryon chemical potential already at T~155 MeV.